A social scientist suspects that the mean number of years of education for adults in a

A social scientist suspects that the mean number of years of education μ for adults in a certain large city is greater than 12 years. She will test the null hypothesis H0 : μ =12 against the alternate hypothesis H1: μ > 12.

She surveys a random sample of 100 adults and finds that the sample mean number of years is x̄ = 12.98. Assume that the standard deviation for the number of years of education is σ = 3 years.

a. Compute the value of the test statistic.

b. Compute the P-value.

c. Interpret the P-value.

d. Is H0 rejected at the α = 0.05 level? State a conclusion.

e. Is H0 rejected at the α = 0.01 level? State a conclusion.